INFLUENCE ANALYSIS ON EXPONENTIAL NONLINEAR MODELS WITH RANDOM EFFECTS

This paper presents a unified diagnostic method for exponential nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991. The authors show that the case deletion model is equivalent to mean shift outlier model. From this point of view, several diagnostic measures, such as Cook distance, score statistics are derived. The local influence measure of Cook is also presented. Numerical example illustrates that our method is available.

Parameter estimation in exponential models by linear and nonlinear fitting methods

Estimation of unknown parameters in exponential models by linear and nonlinear fitting methods is discussed. Based on the extreme value theorem and Taylor series expansion, it is proved theoretically that the parameters estimated by the linear fitting method alone cannot minimize the sum of the squared residual errors in the measurement data when measurement noise is involved in the data. Numerical simulation is performed to compare the performance of the linear and nonlinear fitting methods. Simulation results show that the linear method can obtain only a suboptimal estimate of the unknown parameters and that the nonlinear method gives more accurate results. Application of the fitting methods is demonstrated where the water spectral attenuation coefficient is estimated from underwater images and imaging distances, which supports the improvement in the accuracy of parameter estimation by the nonlinear fitting method.

GEOMETRY OF EXPONENTIAL TYPE REGRESSION MODELS AND ITS ASYMPTOTIC INFERENCE

In this paper, exponential type regression models are considered from geometric point of view. The stochastic expansions relating to the estimate are derived and are used to study several asymptotic inference problems. The biases and the covariances relating to the estimate may be calculated based on the expansions. The information loss of the estimate and a limit theorem connected with the observed and expected Fisher informations are obtained in terms of the curvatures.

Finite Element Implementation of the Exponential Drucker-Prager Plasticity Model for Adhesive Joints

This paper deals with the numerical implementation of the exponential Drucker-Parger plasticitymodel in the commercial finite element software,ABAQUS,via user subroutine UMAT for adhesive joint simulations.The influence of hydrostatic pressure on adhesive strength was investigated by a modified Arcan fixture designed particularly to induce a different state of hydrostatic pressure within an adhesive layer.The developed user subroutine UMAT,which utilizes an associated plastic flow during a plastic deformation,can provide a good agreement between the simulations and the experimental data.Better numerical stability at highly positive hydrostatic pressure loads for a very high order of exponential function can also be achieved compared to when a non-associated flow is used.

Influencing Factors and Prediction of Risk of Returning to Ecological Poverty in Liupan Mountain Region,China

China has resolved its overall regional poverty in 2020 by attaining moderate societal prosperity.The country has entered a new development stage designed to achieve its second centenary goal.However,ecological fragility and risk susceptibility have increased the risk of returning to ecological poverty.In this paper,the Liupan Mountain Region of China was used as a case study,and the counties were used as the scale to reveal the spatiotempora differentiation and influcing factors of the risk of returning to poverty in study area.The indicator data for returning to ecological poverty from 2011-2020 were collected and summarized in three dimensions:ecological,economic and social.The autoregressive integrated moving average model(ARIMA)time series and exponential smoothing method(ES)were used to predict the multidimensional indicators of returning to ecological poverty for 61 counties(districts)in the Liupan Mountain Region for 2021-2030.The back propagation neural network(BPNN)and geographic information system(GIS)were used to generate the spatial distribution and time variation for the index of the risk of returning to ecological poverty(RREP index).The results show that 1)ecological factors were the main factors in the risk of returning to ecological poverty in Liupan Mountain Region.2)The RREP index for the 61 counties(districts)exhibited a downward trend from 2021-2030.The RREP index declined more in medium-and high-risk areas than in low-risk areas.From 2021 to 2025,the RREP index exhibited a slight downward trend.From 2026 to2030,the RREP index was expected to decline faster,especially from 2029-2030.3)Based on the RREP index,it can be roughly divided into three types,namely,the high-risk areas,the medium-risk areas,and the low-risk areas.The natural resource conditions in lowrisk areas of returning to ecological poverty,were better than those in medium-and high-risk areas.

Predicting dynamics of soil organic carbon mineralization with a double exponential model in different forest belts of China

The dynamics of soil organic carbon （SOC） was analyzed by using laboratory incubation and double exponential model that mineralizable SOC was separated into active carbon pools and slow carbon pools in forest soils derived from Changbai and Qilian Mountain areas. By analyzing and fitting the CO2 evolved rates with SOC mineralization, the results showed that active carbon pools accounted tor 1.0% to 8.5% of SOC with an average of mean resistant times （MRTs） for 24 days, and slow carbon pools accounted for 91% to 99% of SOC with an average of MRTs for 179 years. The sizes and MRTs of slow carbon pools showed that SOC in Qilian Mountain sites was more difficult to decompose than that in Changbai Mountain sites. By analyzing the effects of temperature, soil clay content and elevation on SOC mineralization, results indicated that mineralization of SOC was directly related to temperature and that content of accumulated SOC and size of slow carbon pools from Changbai Mountain and Qilian Mountain sites increased linearly with increasing clay content, respectively, which showed temperature and clay content could make greater effect on mineralization of SOC.

Exponential flux-controlled memristor model and its floating emulator

As commercial memristors are still unavailable in the market, mathematic models and emulators which can imitate the features of the mernristor are meaningful for further research. In this paper, based on the analyses of characteristics of the q-φ curve, an exponential flux-controlled model, which has the quality that its memductance （memristance） will keep monotonically increasing or decreasing unless the voltage＇s polarity reverses （if not approach the boundaries）, is constructed. A new approach to designing the floating emulator of the memristor is also proposed. This floating structure can flexibly meet various demands for the current through the memristor （especially the demand for a larger current）. The simulations and experiments are presented to confirm the effectiveness of this model and its floating emulator.

Valuing Credit Default Swap under a double exponential jump diffusion model

This paper discusses the valuation of the Credit Default Swap based on a jump market, in which the asset price of a firm follows a double exponential jump diffusion process, the value of the debt is driven by a geometric Brownian motion, and the default barrier follows a continuous stochastic process. Using the Gaver-Stehfest algorithm and the non-arbitrage asset pricing theory, we give the default probability of the first passage time, and more, derive the price of the Credit Default Swap.

Switching mechanism for TiO_2 memristor and quantitative analysis of exponential model parameters

The memristor, as the fourth basic circuit element, has drawn worldwide attention since its physical implementation was released by HP Labs in 2008. However, at the nano-scale, there are many difficulties for memristor physical realization. So a better understanding and analysis of a good model will help us to study the characteristics of a memristor. In this paper, we analyze a possible mechanism for the switching behavior of a memristor with a Pt/TiO2/Pt structure, and explain the changes of electronic barrier at the interface of Pt/TiO2. Then, a quantitative analysis about each parameter in the exponential model of memristor is conducted based on the calculation results. The analysis results are validated by simulation results. The efforts made in this paper will provide researchers with theoretical guidance on choosing appropriate values for(α, β, χ, γ) in this exponential model.

Fast Fourier Transform Approximation of Foreign Currency Option Pricing Based on Exponential Lévy Model

To study the approximation of foreign currency option prices when the underlying assets＇ price dynamics are described by exponential Lévy processes, the convolution representations for option pricing formulas were given, and then the fast Fourier transform （FFT） algorithm was used to get the approximate values of option prices. Finally, a numerical example was given to demonstrate the calculate steps to the option price by FFT.

Estimation of the Piecewise Exponential Model by Bayesian P-Splines via Gibbs Sampling: Robustness and Reliability of Posterior Estimates

In the investigation of disease dynamics, the effect of covariates on the hazard function is a major topic. Some recent smoothed estimation methods have been proposed, both frequentist and Bayesian, based on the relationship between penalized splines and mixed models theory. These approaches are also motivated by the possibility of using automatic procedures for determining the optimal amount of smoothing. However, estimation algorithms involve an analytically intractable hazard function, and thus require ad-hoc software routines. We propose a more user-friendly alternative, consisting in regularized estimation of piecewise exponential models by Bayesian P-splines. A further facilitation is that widespread Bayesian software, such as WinBUGS, can be used. The aim is assessing the robustness of this approach with respect to different prior functions and penalties. A large dataset from breast cancer patients, where results from validated clinical studies are available, is used as a benchmark to evaluate the reliability of the estimates. A second dataset from a small case series of sarcoma patients is used for evaluating the performances of the PE model as a tool for exploratory analysis. Concerning breast cancer data, the estimates are robust with respect to priors and penalties, and consistent with clinical knowledge. Concerning soft tissue sarcoma data, the estimates of the hazard function are sensitive with respect to the prior for the smoothing parameter, whereas the estimates of regression coefficients are robust. In conclusion, Gibbs sampling results an efficient computational strategy. The issue of the sensitivity with respect to the priors concerns only the estimates of the hazard function, and seems more likely to occur when non-large case series are investigated, calling for tailored solutions.

Estimation of Natural Gas Production,Import and Consumption in Brazil Based on Three Mathematical Models

A mathematical model capable of providing a forecast of future consumption and import of natural gas is essential for the planning of the Brazilian energy matrix. The aim of this study is to compare three mathematical models, logistic model or model of Verhulst, exponential model or the model of Malthus and the model of von Bertalanffy to analyze the possibilities of these models to describe the evolution of production, import and consumption of natural gas in Brazil, from data provided by the energy balance of the Ministry of Mines and Energy (MME) from 1970 to 2009. A projection of the production and the import of natural gas up to 2017 is made with the models studied in this article and compared with the Brazilian Ten-Year Plan for Expansion of Energy (PDE). At the end of this paper a comparison with the Hubbert model for Brazilian natural gas production is made. These data were adjusted to use the differential equations which describe the models of population growth. All the computer work used in this article: graphics, resolution of differential equations, calculations of linearization and the least squares fitting was prepared in the software MatLab. The results obtained by means of graphs show that the population dynamics models (logistic, exponential and von Bertalanffy) can be applied in modeling the production, import and consumption of natural gas in Brazil.

Forecasting Stock Prices with an Integrated Approach Combining ARIMA and Machine Learning Techniques ARIMAML

Stock market prediction has long been an area of interest for investors, traders, and researchers alike. Accurate forecasting of stock prices is crucial for financial decision-making and risk management. This paper presents a novel approach to predict stock prices by integrating Autoregressive Integrated Moving Average (ARIMA) and Exponential smoothing and Machine Learning (ML) techniques. Our study aims to enhance the predictive accuracy of stock price forecasting, which can significantly impact investment strategies and economic growth in this research paper implement the ARIMAML proposed method to predict the stock prices for Investment Bank of Iraq.

Local Trade Networks among Farmers and Traders

Both farmers and traders benefit from trade networking, which is crucial for the local economy. Therefore, it is crucial to understand how these networks operate, and how they can be managed more effectively. Throughout this study, we examine the economic networks formed between farmers and traders through the trade of food products. These networks are analyzed from the perspective of their structure and the factors that influence their development. Using data from 18 farmers and 15 traders, we applied exponential random graph models. The results of our study showed that connectivity, Popularity Spread, activity spread, good transportation systems, and high yields all affected the development of networks. Therefore, farmers’ productivity and high market demand can contribute to local food-crop trade. The network was not affected by reciprocity, open markets, proximity to locations, or trade experience of actors. Policy makers should consider these five factors when formulating policies for local food-crop trade. Additionally, local actors should be encouraged to use these factors to improve their network development. However, it is important to note that these factors alone cannot guarantee success. Policy makers and actors must also consider other factors such as legal frameworks, economic policies, and resource availability. Our approach can be used in future research to determine how traders and farmers can enhance productivity and profit in West Africa. This study addresses a research gap by examining factors influencing local food trade in a developing country.

Coherence of wind pressure on domes

The concept of the coherence function is adopted to find the wind pressure correlation of two points on domes of different rise-span ratios. The pressure measurements are made on the dome roof models by the wind tunnel test. The coherence functions for different separation distances at several directions of the domes from different wind directions are examined. The results show that there is a strong correlation for two adjacent points at low frequency, but not for non-adjacent points. The coherence of the wind pressure increases with the decrease in the separation distance. Moreover, the coherence of the wind pressure is in the strongest correlation on the along-wind direction at the same separation, but the lowest correlation is on the cross-wind direction. The detailed derivation of the proposed exponential coherence model of the wind pressure from experimental data is also discussed. It is found that the proposed exponential coherence model can be appropriate, especially, for small separations and the change in the directions on domes. Based on the quasi-steady theory, the relationship between the wind pressure and the wind velocity on the basis of the coherence model is also examined. The coherence observed between the wind pressure and the wind velocity is not adequately predicted by the quasi-steady theory.

Calibration of Soil Electromagnetic Conductivity in Inverted Salinity Profiles with an Integration Method

Various calibration methods have been propounded to determine profiles of apparent bulk soil electrical conductivity (ECa) and soil electrical conductivity of a saturated soil paste extract (ECe) or a 1:5 soil water extract (EC1:5) using an electromagnetic induction instrument (EM38). The modeled coefficients, one of the successful and classical methods hitherto, were chosen to calibrate the EM38 measurements of the inverted salinity profiles of characteristic coastal saline soils at selected sites of Xincao Farm, Jiangsu Province, China. However, this method required three parameters for each depth layer. An integration approach, based on an exponential decay profile model, was proposed and the model was fitted to all the calibration sites. The obtained model can then be used to predict EC1:5 at a certain depth from electromagnetic measurements made using the EM38 device positioned in horizontal and vertical positions at the soil surface. This exponential decay model predicted the EC1:5 well according to the results of a one-way analysis of variance, and the further comparison indicated that the modeled coefficients appeared to be slightly superior to, but not statistically different from, this exponential decay model. Nevertheless, this exponential decay model was more significant and practical because it depended on less empirical parameters and could be used to perform point predictions of EC1:5 continuously with depth.

Modulation of neuronal dynamic range using two different adaptation mechanisms

The capability of neurons to discriminate between intensity of external stimulus is measured by its dynamic range.A larger dynamic range indicates a greater probability of neuronal survival.In this study,the potential roles of adaptation mechanisms（ion currents） in modulating neuronal dynamic range were numerically investigated.Based on the adaptive exponential integrate-and-fire model,which includes two different adaptation mechanisms,i.e.subthreshold and suprathreshold（spike-triggered） adaptation,our results reveal that the two adaptation mechanisms exhibit rather different roles in regulating neuronal dynamic range.Specifically,subthreshold adaptation acts as a negative factor that observably decreases the neuronal dynamic range,while suprathreshold adaptation has little influence on the neuronal dynamic range.Moreover,when stochastic noise was introduced into the adaptation mechanisms,the dynamic range was apparently enhanced,regardless of what state the neuron was in,e.g.adaptive or non-adaptive.Our model results suggested that the neuronal dynamic range can be differentially modulated by different adaptation mechanisms.Additionally,noise was a non-ignorable factor,which could effectively modulate the neuronal dynamic range.

Notes on M-Estimation in Exponential Signal Models

An M-estimation of the parameters in an undamped exponential signal model was proposed in Wu and Tam(IEEE Trans Signal Process 49(2):373–380,2001),and the estimation was shown to be consistent under mild assumptions.In this paper,the limiting distributions of the M-estimators are investigated.It is shown that they are asymptotically normally distributed under similar conditions as assumed in Wu and Tam(IEEE Trans Signal Process 49(2):373–380,2001).In addition,a recursive algorithm for computing the M-estimators of frequencies is proposed,and the strong consistency of these estimators is established.Monte Carlo simulation studies using Huber’sρfunction are also provided.

The growth of the Rhodococcus sp. on diesel fuel under the effect of heavy metals and different concentrations of zinc

Co-contamination of diesel fuel and heavy metals can be challenging for microbial remediation due to the complex composition of the fuel and the inhibitory effect of heavy metals.There is an urgent need to study this interaction to improve the pollutant removal efficiency in the Polar Regions.The growth of an Antarctic bacterium,Rhodococcus sp.was studied by comparing the growth at the logarithmic phase under the effect of selected heavy metals(Pb,Cr,As,Cd,Cu,Zn,Ni,Hg and Co).The selected heavy metals inhibited the growth of the Rhodococcus sp.on diesel fuel in an order from highest to lowest of:Hg>Zn>Cd>Cu>Co>Ni>As>Pb>Cr.Growth on diesel fuel co-contaminated with Hg and Zn were 2.95%and 5.71%,respectively compared to the no-metal control.A further experiment with various Zn concentrations was conducted.The specific growth rate of Rhodococcus sp.co-contaminated with different concentrations of Zn showed a correlation coefficient(r)of 0.916,and was modelled with an exponential decay model.Additional investigation is needed to determine the effect of low concentration of Zn on hydrocarbon degradation.It is important to understand the relationships between microbes,hydrocarbons and heavy metals,especially in the Polar Regions because this interaction might be promising in treating hydrocarbon-polluted sites containing heavy metals.The data and results also provide baseline tools of bioremediation processes at low temperatures and the knowledge of the ecological roles of Rhodococcus sp.in Antarctica.

The M2 Money Supply, the Economy, and the National Debt: A Mathematical Approach

The United States dollar was tied to a finite standard dating back to 1792. The dollar has survived multiple wars, armed conflicts short of war, economic recessions, and the Great Depression. At the end of World War II, the dollar, by international agreement, effectively became the world’s reserve currency. Other currencies were fixed to the dollar and the dollar was in turn fixed to the gold standard, that is, the value of a dollar was fixed at thirty-five dollars per ounce of gold. In 1971, the United States government severed the dollar from the gold standard leaving the size of the money supply free of any finite limit. Since that time, the United States money supply, national debt, and stock market indices have experienced exponential growth. The purpose of this paper is to investigate mathematically and model the relationship among these key economic indicators. Our work in this paper allows us to gain some insight into how each of these economic indicators can influence one another while giving us a better idea of how the economy functions. We were allowed to collect data for each of the indicators over a certain period which allowed us to demonstrate that a strong correlation exists among these three indicators. After collecting our data and making some logical assumptions, we modeled the money supply as a function of time. In turn, we modeled the Dow Jones stock market index as a function of the money supply. Finally, we produced a model of the National Debt as a function of the Dow Jones stock market index. From the data, we collected and our economic indicator models, we derived a series of differential equations that would help us observe the exponential growth trend of each graphically. By showing a comparison from our collection of raw data versus our results from our model, we conclude that, under prevailing circumstances, it is reasonable to expect growth in all three indicators and increasing market volatility for some time to come. We have answered the question of whether the monetary and fiscal policies of the past half-century have been of some benefit. However, we question whether this trend is good for all Americans and whether it is sustainable in perpetuity. This paper concludes with possible areas of interest warranting additional investigation to enable us to better understand the economy and develop effective financial strategies.